The 'mutual' and the 'self' in terms of the 'conjugacy' of Euclidean and Minkowski Weyl fermions

Let the spacetime metric have signature $(s,t)$.

1. Mutual conjugated means that the left and right Weyl representations are each other's complex conjugate complex representations. This happens if $s-t~=~2mod 4$.

2. Self-conjugated means that the left and right Weyl representations are (pseudo) real representations. This happens if $s-t~=~0mod 4$.

(Weyl representations only exist in even spacetime dimensions $s+t~=~0mod 2$.)